Final answer:
The marginal revenue product of labor (MRPL) for a monopolist facing a competitive labor market can be calculated by finding the derivative of the production function with respect to labor and multiplying it by the price of the output. The equilibrium amount of labor hired and the equilibrium wage can be determined by the intersection of supply and demand for labor. Plotting the supply and demand curves will provide a visual representation of the equilibrium values.
Step-by-step explanation:
To find the marginal revenue product of labor (MRPL) for a monopolist facing a competitive labor market, we need to calculate the marginal product of labor (MPL). The MPL is the derivative of the production function with respect to labor. In this case, the production function is Q=10L⁰⋅⁵K⁰⋅⁵, where K is fixed at 1. Taking the derivative of the production function with respect to L, we get MPL=5L⁰⋅⁴K⁰⋅⁵.
To find the MRPL, we multiply the MPL by the price of the output, which in this case is P=100−Q. Substituting the MPL into the price equation, we get MRPL=(100−Q)⋅MPL=(100−10L⁰⋅⁵K⁰⋅⁵)⋅(5L⁰⋅⁴K⁰⋅⁵)=(500L⁰⋅⁴−50L⁰⋅⁵)K⁰⋅⁵.
The equilibrium amount of labor hired and the equilibrium wage can be determined by the intersection of supply and demand for labor. The supply of labor curve represents the marginal cost of labor, which is equal to the wage rate. The demand for labor curve represents the MRPL. The equilibrium occurs where supply equals demand.
Plotting the supply and demand curves with the correct intercepts and equilibrium values will provide a visual representation of the equilibrium amount of labor hired and the equilibrium wage.